Упростить выражение. 1/(sina+sin3a) + 1/(sin3a+sin5a)

1/(sin a + sin 3a) + 1/(sin 3a + sin 5a) = 1/(2 sin 2a cos a) + 1/(2 sin 4a cos a) = 1/(2 cos a) (1/sin 2a + 1/sin 4a) = 1/(2 cos a) (1/(sin 2a) + (1/(2 sin 2a cos 2a)) = (1/(4 sin 2a cos a)) (1 + 1/cos 2a) = (1/(8 sin a cos^2 a)) (1 + 1/(cos^2a - sin^2a )) = (1/(8 sin a cos^2 a)) ((cos^2 a - sin^2 a + cos^2 a + sin^2 a)/(cos^2 a - sin^2 a) = (1/(8 sin a cos^2 a)) ((2 cos^2 a)/(cos^2 a - sin^2 a))=1/(sin a (cos^2 a - sin^2 a)) = 1/(sin a cos 2a).